Controlled Markov Processes and Viscosity SolutionsThis book is intended as an introduction to optimal stochastic control for continuous time Markov processes and to the theory of viscosity solutions. |
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Page 125
Wendell Helms Fleming, H. Mete Soner. III Optimal Control of Markov Processes : Classical Solutions III.1 Introduction The purpose of this chapter is to give a concise , nontechnical introduction to optimal stochastic control for Markov ...
Wendell Helms Fleming, H. Mete Soner. III Optimal Control of Markov Processes : Classical Solutions III.1 Introduction The purpose of this chapter is to give a concise , nontechnical introduction to optimal stochastic control for Markov ...
Page 136
... processes which are not Markov , or which are Markov on a higher dimensional state space . For a treatment of such situations and applications in communications engineering , see [ Ku2 ] . III.6 Controlled Markov processes We now ...
... processes which are not Markov , or which are Markov on a higher dimensional state space . For a treatment of such situations and applications in communications engineering , see [ Ku2 ] . III.6 Controlled Markov processes We now ...
Page 275
... processes In this section we shall outline how to extend some of the results described in Sections 2-5 for Markov diffusion processes to other classes of Markov processes . These results are based mainly on Sheu [ Sh1 ] . Following the ...
... processes In this section we shall outline how to extend some of the results described in Sections 2-5 for Markov diffusion processes to other classes of Markov processes . These results are based mainly on Sheu [ Sh1 ] . Following the ...
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Controlled Markov Processes and Viscosity Solutions Wendell H. Fleming,Halil Mete Soner Limited preview - 2006 |
Controlled Markov Processes and Viscosity Solutions Wendell H. Fleming,Halil Mete Soner No preview available - 2006 |
Common terms and phrases
admissible control assume assumptions boundary condition boundary data bounded c₁ Cą(Q calculus of variations Chapter classical solution consider constant continuous on Q convergence convex Corollary cylindrical region defined definition denote dynamic programming equation dynamic programming principle Dynkin formula Example exists exit finite first-order formulation Hamilton-Jacobi equation Hence HJB equation holds implies inequality initial data lateral boundary Lemma lim sup linear Lipschitz continuous Markov chain Markov control policy Markov processes maximum principle minimizing Moreover nonlinear obtain optimal control optimal control problem partial derivatives partial differential equation proof of Theorem prove result satisfies second-order Section semigroup stochastic differential equation Suppose t₁ test function Theorem 5.1 uniformly continuous unique value function variations problem Verification Theorem viscosity solution viscosity subsolution viscosity supersolution yields